For every pair of objects a and b in C a FullFaithfulFunctorF : C -> D maps every morphism
f : a -> b onto a distinct morphism f : T a -> T b (since it is faithful) and every morphism from
g : T a -> T b can be obtained from some f. (It maps Hom-sets bijectively, or in short fmap has both
a left and right inverse under composition.